You can access the course materials quickly from

www.gerkovink.com/fundamentals

1. apply and interpret the basic methodological and statistical concepts that are associated with doing predictive and/or inferential research;
2. apply and interpret important techniques in linear and logistic regression analysis;

This means that you will learn the ins and outs of inferential and predictive research with linear and logistic models.

• what this all covers will become clear during the course
• we will learn R to perform our data analysis and visualizations
• we will learn the math and skills behind these ubiquitous modeling techniques
• we will also learn the assumptions of (logistic) regression models

Learn to keep your cool

and build the foundation for a succesfull scripting career in predictive and inferential analytics

• R is a language and environment for statistical computing and for graphics

• GNU project (100% free software)

• Managed by the R Foundation for Statistical Computing, Vienna, Austria.

• Community-driven

• Based on the object-oriented language S (1975)

• Aggregates all convenient information and procedures into one single place
• Allows you to work in projects
• Manages your code with highlighting
• Gives extra functionality (Shiny, knitr, markdown, LaTeX)
• Allows for integration with version control routines, such as Git.

• R works with objects that consist of elements. The smallest elements are numbers and characters.

  • These elements are assigned to objects.
  • A set of objects can be used to perform calculations
  • Calculations can be presented as functions
  • Functions are used to perform calculations and return new objects, containing calculated (or estimated) elements.

• Everything that is published on the Comprehensive R Archive Network (CRAN) and is aimed at R users, must be accompanied by a help file.
• If you know the name of the function that performs an operation, e.g. anova(), then you just type ?anova or help(anova) in the console.

• If you do not know the name of the function: type ?? followed by your search criterion. For example ??anova returns a list of all help pages that contain the word ‘anova’

• Alternatively, the internet will tell you almost everything you’d like to know and sites such as http://www.stackoverflow.com and http://www.stackexchange.com, as well as Google can be of tremendous help.
  • If you google R related issues; use ‘R:’ as a prefix in your search term

• Assigning things in R is very straightforward:

  • you just use <-

• For example, if you assign the value 100 (an element) to object a, you would type

a <- 100

• Calling things in R is also very straightforward:

  • you just use type the name you have given to the object

• For example, we assigned the value 100 to object a. To call object a, we would type

a

## [1] 100

This is why we use R-Studio.

• We can assign more than one element to a vector (in this case a 1-dimensional congatenation of numbers 1 through 5)

a <- c(1, 2, 3, 4, 5)
a

## [1] 1 2 3 4 5

b <- 1:5
b

## [1] 1 2 3 4 5

Characters (or character strings) in R are indicated by the double quote identifier.

a.new <- c(a, "A")
a.new

## [1] "1" "2" "3" "4" "5" "A"

Notice the difference with a from the previous slide

a

## [1] 1 2 3 4 5

rep(a, 15)

##  [1] 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
## [36] 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
## [71] 1 2 3 4 5

If we would want just the third element, we would type

a[3]

## [1] 3

This we would refer to as a matrix

c <- matrix(a, nrow = 5, ncol = 2)
c

##      [,1] [,2]
## [1,]    1    1
## [2,]    2    2
## [3,]    3    3
## [4,]    4    4
## [5,]    5    5

• The first row is called by

c[1, ]

## [1] 1 1

• The second column is called by

c[, 2]

## [1] 1 2 3 4 5

• The intersection of the first row and second column is called by

c[1, 2]

## [1] 1

In short; square brackets [] are used to call elements, rows, columns (and much more beyond the scope of this course)

If we add a character column to matrix c; everything becomes a character:

cbind(c, letters[1:5])

##      [,1] [,2] [,3]
## [1,] "1"  "1"  "a" 
## [2,] "2"  "2"  "b" 
## [3,] "3"  "3"  "c" 
## [4,] "4"  "4"  "d" 
## [5,] "5"  "5"  "e"

Alternatively,

cbind(c, c("a", "b", "c", "d", "e"))

##      [,1] [,2] [,3]
## [1,] "1"  "1"  "a" 
## [2,] "2"  "2"  "b" 
## [3,] "3"  "3"  "c" 
## [4,] "4"  "4"  "d" 
## [5,] "5"  "5"  "e"

Remember, matrices and vectors are numerical OR character objects. They can never contain both and still be used for numerical calculations.

d <- data.frame("V1" = rnorm(5),
                "V2" = rnorm(5, mean = 5, sd = 2), 
                "V3" = letters[1:5])
d

##            V1       V2 V3
## 1  0.08277864 5.849016  a
## 2  0.54542935 3.292187  b
## 3  0.19208169 2.294143  c
## 4 -0.65761705 2.523033  d
## 5 -0.85008235 4.005873  e

We ‘filled’ a dataframe with two randomly generated sets from the normal distribution - where \(V1\) is standard normal and \(V2 \sim N(5,2)\) - and a character set.

Data frames can contain both numerical and character elements at the same time, although never in the same column.

You can name the columns and rows in data frames (just like in matrices)

row.names(d) <- c("row 1", "row 2", "row 3", "row 4", "row 5")
d

##                V1       V2 V3
## row 1  0.08277864 5.849016  a
## row 2  0.54542935 3.292187  b
## row 3  0.19208169 2.294143  c
## row 4 -0.65761705 2.523033  d
## row 5 -0.85008235 4.005873  e

There are two ways to obtain row 3 from data frame d:

d["row 3", ]

##              V1       V2 V3
## row 3 0.1920817 2.294143  c

and

d[3, ]

##              V1       V2 V3
## row 3 0.1920817 2.294143  c

The intersection between row 2 and column 4 can be obtained by

d[2, 3]

## [1] b
## Levels: a b c d e

Both

d[, "V2"] # and

## [1] 5.849016 3.292187 2.294143 2.523033 4.005873

d[, 2]

## [1] 5.849016 3.292187 2.294143 2.523033 4.005873

yield the second column. But we can also use $ to call variable names in data frame objects

d$V2

## [1] 5.849016 3.292187 2.294143 2.523033 4.005873

If you wish to use numerical objects that have more than two dimension, an array would be a suitable object. The following code yields a 3-dimensional array (2 rows, 4 columns and 3 matrices):

e <- array(1:24, dim = c(2, 4, 3))
e

## , , 1
## 
##      [,1] [,2] [,3] [,4]
## [1,]    1    3    5    7
## [2,]    2    4    6    8
## 
## , , 2
## 
##      [,1] [,2] [,3] [,4]
## [1,]    9   11   13   15
## [2,]   10   12   14   16
## 
## , , 3
## 
##      [,1] [,2] [,3] [,4]
## [1,]   17   19   21   23
## [2,]   18   20   22   24

The square bracket identification works similarly to the identification of matrices and dataframes, but with the added dimension(s). For example,

e[1, 3, 2]

## [1] 13

yields the element in the first row of the third column in the second matrix. This is exactly the downside to an array: it is a series of matrices.

In other words, characters and numerical elements may not be mixed.

If we replace the third matrix in the array by a character version of that matrix, we obtain

e[, , 3] <- as.character(e[, , 3])
e

## , , 1
## 
##      [,1] [,2] [,3] [,4]
## [1,] "1"  "3"  "5"  "7" 
## [2,] "2"  "4"  "6"  "8" 
## 
## , , 2
## 
##      [,1] [,2] [,3] [,4]
## [1,] "9"  "11" "13" "15"
## [2,] "10" "12" "14" "16"
## 
## , , 3
## 
##      [,1] [,2] [,3] [,4]
## [1,] "17" "19" "21" "23"
## [2,] "18" "20" "22" "24"

List are just what it says they are: lists. You can have a list of everything mixed with everything. For example, an simple list can be created by

f <- list(a)
f

## [[1]]
## [1] 1 2 3 4 5

Elements or objects within lists can be called by using double square brackets [[]]. For example, the first (and only) element in list f is object a

f[[1]]

## [1] 1 2 3 4 5

We can simply add an object or element to an existing list

f[[2]] <- d
f

## [[1]]
## [1] 1 2 3 4 5
## 
## [[2]]
##                V1       V2 V3
## row 1  0.08277864 5.849016  a
## row 2  0.54542935 3.292187  b
## row 3  0.19208169 2.294143  c
## row 4 -0.65761705 2.523033  d
## row 5 -0.85008235 4.005873  e

to obtain a list with a vector and a data frame.

We can add names to the list as follows

names(f) <- c("vector", "data frame")
f

## $vector
## [1] 1 2 3 4 5
## 
## $`data frame`
##                V1       V2 V3
## row 1  0.08277864 5.849016  a
## row 2  0.54542935 3.292187  b
## row 3  0.19208169 2.294143  c
## row 4 -0.65761705 2.523033  d
## row 5 -0.85008235 4.005873  e

Calling the vector (a) from the list can be done as follows

f[[1]]

## [1] 1 2 3 4 5

f[["vector"]]

## [1] 1 2 3 4 5

f$vector

## [1] 1 2 3 4 5

Take the following example

g <- list(f, f)

To call the vector from the second list within the list g, use the following code

g[[2]][[1]]

## [1] 1 2 3 4 5

g[[2]]$vector

## [1] 1 2 3 4 5

• Logical operators are signs that evaluate a statement, such as ==, <, >, <=, >=, and | (OR) as well as & (AND). Typing ! before a logical operator takes the complement of that action. There are more operations, but these are the most useful.

• For example, if we would like elements out of matrix c that are larger than 3, we would type:

c[c > 3]

## [1] 4 5 4 5

c > 3

##       [,1]  [,2]
## [1,] FALSE FALSE
## [2,] FALSE FALSE
## [3,] FALSE FALSE
## [4,]  TRUE  TRUE
## [5,]  TRUE  TRUE

The column values for TRUE may be of different length. A vector as a return is therefore more appropriate.

• If we would like the elements that are smaller than 3 OR larger than 3, we could type

c[c < 3 | c > 3] #c smaller than 3 or larger than 3

## [1] 1 2 4 5 1 2 4 5

or

c[c != 3] #c not equal to 3

## [1] 1 2 4 5 1 2 4 5

• In fact, c != 3 returns a matrix

##       [,1]  [,2]
## [1,]  TRUE  TRUE
## [2,]  TRUE  TRUE
## [3,] FALSE FALSE
## [4,]  TRUE  TRUE
## [5,]  TRUE  TRUE

• Remember c?:

##      [,1] [,2]
## [1,]    1    1
## [2,]    2    2
## [3,]    3    3
## [4,]    4    4
## [5,]    5    5

• Things that have no representation in real number space (at least not without tremendous effort)
  • For example, the following code returns “Not a Number”

0 / 0

## [1] NaN

• Also impossible are calculations based on missing values (NA’s)

mean(c(1, 2, NA, 4, 5))

## [1] NA

There are two easy ways to perform “listwise deletion”:

mean(c(1, 2, NA, 4, 5), na.rm = TRUE)

## [1] 3

mean(na.omit(c(1, 2, NA, 4, 5)))

## [1] 3

(3 - 2.9)

## [1] 0.1

(3 - 2.9) <= 0.1

## [1] FALSE

Why does R tell us that 3 - 2.9 \(\neq\) 0.1?

(3 - 2.9) - .1

## [1] 8.326673e-17

• keep your code tidy
• use comments (text preceded by #) to clarify what you are doing
  • If you look at your code again, one month from now: you will not know what you did –> unless you use comments
• when working with functions, use the TAB key to quickly access the help for the function’s components
• work with logically named R-scripts
  • indicate the sequential nature of your work
• work with RStudio projects
• if allowed, place your project folders in some cloud-based environment

There are several ‘layers’ in R. Some layers you are allowed to fiddle around in, some are forbidden. In general there is the following distinction:

• The global environment.
• User environments
• Functions
• Packages
• Namespaces

The global environment can be seen as a olympic-size swimming pool. Everything you do has its place there.

If you’d like, you may create another, separate environment to work in.

• A user environment would by default not have access to other environments

• If you create a function, it is positioned in the global environment.

• Everything that happens in a function, stays in a function. Unless you specifically tell the function to share the information with the global environment.

• See functions as a shampoo bottle in a swimming pool to which you add some water. If you’d like to see the color of the mixture, you’d have to squeeze the bottle for it to come out.

• Packages have their own space.

  • Everything needed to run the functions in a package is needly contained within its own space
  • See packages as separate (mini) pools that are connected to the main pool (the global environment)

There are two ways to load a package in R

library(stats)

and

require(stats)

require() will produce a warning when a package is not found. In other words, it will not stop as function library() does.

The easiest way to install e.g. package mice is to use

install.packages("mice")

Alternatively, you can also do it in RStudio through

Tools --> Install Packages

• Namespaces. These are the deeper layers that feed new water to the surface of the mini pools.
  • Packages can have namespaces.
  • Functions within packages are executed within the package or namespace and have access to the global environment.
  • Objects in the global environment that match objects in the function’s namespace are ignored when running functions from packages!

A workspace contains all changes you made to environments, functions and namespaces.

A saved workspace contains everything at the time of the state wherein it was saved.

You do not need to run all the previous code again if you would like to continue working at a later time.

• You can save the workspace and continue exactly where you left.

Workspaces are compressed and require relatively little memory when stored. The compression is very efficient and beats reloading large datasets from raw text.

R by default saves (part of) the code history and RStudio expands this functionality greatly.

Most often it may be useful to look back at the code history for various reasons.

• There are multiple ways to access the code history.

  1. Use arrow up in the console. This allows you to go back in time, one codeline by one. Extremely useful to go back to previous lines for minor alterations to the code.
  2. Use the history tab in the environment pane. The complete project history can be found here and the history can be searched. This is particularly convenient when you know what code you are looking for.

• Every project has its own history
• Every research project has its own project
• Every project can have its own folder, which also serves as a research archive
• Every project can have its own version control system
• R-studio projects can relate to Git (or other online) repositories

To model objects based on other objects, we use ~ (tilde)

- For example, to model body mass index (BMI) on weight, we would type

BMI ~ weight

Tilde is used to separate the left- and right-hand sides in a model formula.

For functions (or models), within models we use I() - For example, to model body mass index (BMI) on its deterministic function of weight and height, we would type

BMI ~ I(weight / height^2)

Remember the boys data from package mice:

lm(bmi ~ wgt, data = boys)

## 
## Call:
## lm(formula = bmi ~ wgt, data = boys)
## 
## Coefficients:
## (Intercept)          wgt  
##     14.5401       0.0935

Remember the boys data from package mice:

lm(bmi ~ I(wgt / (hgt / 100)^2), data = boys)

## 
## Call:
## lm(formula = bmi ~ I(wgt/(hgt/100)^2), data = boys)
## 
## Coefficients:
##        (Intercept)  I(wgt/(hgt/100)^2)  
##          -0.005553            1.000034

It is ‘nicer’ to store the output from the function in an object. The convention for regression models is an object called fit.

fit <- lm(bmi ~ I(wgt / (hgt / 100)^2), data = boys)

The object fit contains a lot more than just the regression weights. To inspect what is inside you can use

ls(fit)

##  [1] "assign"        "call"          "coefficients"  "df.residual"  
##  [5] "effects"       "fitted.values" "model"         "na.action"    
##  [9] "qr"            "rank"          "residuals"     "terms"        
## [13] "xlevels"

Another approach to inspecting the contents of fit is the function attributes()

attributes(fit)

## $names
##  [1] "coefficients"  "residuals"     "effects"       "rank"         
##  [5] "fitted.values" "assign"        "qr"            "df.residual"  
##  [9] "na.action"     "xlevels"       "call"          "terms"        
## [13] "model"        
## 
## $class
## [1] "lm"

The benefit of using attributes() is that it directly tells you the class of the object.

class(fit)

## [1] "lm"

Classes are used for an object-oriented style of programming. This means that you can write a specific function that - has fixed requirements with respect to the input. - presents output or graphs in a predefined manner.

When a generic function fun is applied to an object with class attribute c("first", "second"), the system searches for a function called fun.first and, if it finds it, applies it to the object.

If no such function is found, a function called fun.second is tried. If no class name produces a suitable function, the function fun.default is used (if it exists). If there is no class attribute, the implicit class is tried, then the default method.

plot(bmi ~ wgt, data = boys)

plot(lm(bmi ~ wgt, data = boys), which = 1)

plot(lm(bmi ~ wgt, data = boys), which = 2)

plot(lm(bmi ~ wgt, data = boys), which = 3)

plot(lm(bmi ~ wgt, data = boys), which = 4)

plot(lm(bmi ~ wgt, data = boys), which = 5)

plot(lm(bmi ~ wgt, data = boys), which = 6)

The function plot() is called, but not used. Instead, because the linear model has class "lm", R searches for the function plot.lm().

If function plot.lm() would not exist, R tries to apply function plot() (which would have failed in this case because plot requires x and y as input)

plot.lm() is created by John Maindonald and Martin Maechler. They thought it would be useful to have a standard plotting environment for objects with class "lm".

Since the elements that class "lm" returns are known, creating a generic function class is straightforward.

File names should end in .R and, of course, be meaningful.

GOOD:

predict_ad_revenue.R

BAD:

foo.R

Don’t use underscores ( _ ) or hyphens ( - ) in identifiers. Identifiers should be named according to the following conventions.

1. The preferred form for variable names is all lower case letters and words separated with dots (variable.name), but variableName is also accepted;
2. function names have initial capital letters and no dots (FunctionName);
3. constants are named like functions but with an initial k.

• variable.name is preferred, variableName is accepted
  GOOD: avg.clicks
  OK: avgClicks
  BAD: avg_Clicks

• FunctionName
  GOOD: CalculateAvgClicks
  BAD: calculate_avg_clicks , calculateAvgClicks
  

• kConstantName

The maximum line length is 80 characters.

# This is to demonstrate that at about eighty characters you would move off of the page

# Also, if you have a very wide function
fit <- lm(age ~ bmi + hgt + wgt + hc + gen + phb + tv + reg + bmi * hgt + wgt * hgt + wgt * hgt * bmi, data = boys)

# it would be nice to pose it as
fit <- lm(age ~ bmi + hgt + wgt + hc + gen + phb + tv + reg + bmi * hgt 
          + bmi * wgt + wgt * hgt + wgt * hgt * bmi, data = boys)
#or
fit <- lm(age ~ bmi + hgt + wgt + hc + gen + phb + tv + reg 
          + bmi * hgt 
          + bmi * wgt
          + wgt * hgt 
          + wgt * hgt * bmi, 
          data = boys)

When indenting your code, use two spaces. RStudio does this for you!

Never use tabs or mix tabs and spaces.

Exception: When a line break occurs inside parentheses, align the wrapped line with the first character inside the parenthesis.

Place spaces around all binary operators (=, +, -, <-, etc.).

Exception: Spaces around =’s are optional when passing parameters in a function call.

lm(age ~ bmi, data=boys)

or

lm(age ~ bmi, data = boys)

Do not place a space before a comma, but always place one after a comma.

GOOD:

tab.prior <- table(df[df$days.from.opt < 0, "campaign.id"])
total <- sum(x[, 1])
total <- sum(x[1, ])

BAD:

# Needs spaces around '<'
tab.prior <- table(df[df$days.from.opt<0, "campaign.id"])  
# Needs a space after the comma
tab.prior <- table(df[df$days.from.opt < 0,"campaign.id"])  
# Needs a space before <-
tab.prior<- table(df[df$days.from.opt < 0, "campaign.id"]) 
# Needs spaces around <-
tab.prior<-table(df[df$days.from.opt < 0, "campaign.id"])  
# Needs a space after the comma
total <- sum(x[,1])  
# Needs a space after the comma, not before 
total <- sum(x[ ,1])  

Place a space before left parenthesis, except in a function call.

GOOD:

if (debug)

BAD:

if(debug)

Extra spacing (i.e., more than one space in a row) is okay if it improves alignment of equals signs or arrows (<-).

plot(x    = x.coord,
     y    = data.mat[, MakeColName(metric, ptiles[1], "roiOpt")],
     ylim = ylim,
     xlab = "dates",
     ylab = metric,
     main = (paste(metric, " for 3 samples ", sep = "")))

Do not place spaces around code in parentheses or square brackets.

Exception: Always place a space after a comma.

GOOD:

if (debug)
x[1, ]

BAD:

if ( debug )  # No spaces around debug
x[1,]  # Needs a space after the comma 

• Use common sense and BE CONSISTENT.

• The point of having style guidelines is to have a common vocabulary of coding
  • so people can concentrate on what you are saying, rather than on how you are saying it.

• If code you add to a file looks drastically different from the existing code around it, the discontinuity will throw readers out of their rhythm when they go to read it. Try to avoid this.